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Chapter 4: Problem 7

A dragster starts from rest and reaches a speed of \(62.5 \mathrm{~m} / \mathrm{s}\) in \(10.0 \mathrm{~s}\). Find its acceleration (in \(\mathrm{m} / \mathrm{s}^{2}\) ).

Short Answer

Expert verified
The acceleration of the dragster is 6.25 \(\text{m/s}^2\).

Step by step solution

01

Define the Initial Conditions

The dragster starts from rest, which means its initial velocity \( u \) is \( 0 \ \text{m/s} \). It reaches a final velocity \( v \) of \( 62.5 \ \text{m/s} \) in a time \( t \) of \( 10.0 \ \text{s} \). We need to find the acceleration \( a \).
02

Use the Formula for Acceleration

The formula to calculate acceleration when you know the initial velocity, final velocity, and time is:\[ a = \frac{v - u}{t} \]Substitute the known values into the equation: \( v = 62.5 \ \text{m/s} \), \( u = 0 \ \text{m/s} \), and \( t = 10.0 \ \text{s} \).
03

Substitute and Calculate

Substitute the values into the formula to find acceleration:\[ a = \frac{62.5 \, \text{m/s} - 0 \, \text{m/s}}{10.0 \, \text{s}} \]\[ a = \frac{62.5}{10.0} \]\[ a = 6.25 \, \text{m/s}^2 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Physics Problems
When tackling physics problems, it's important to break down the situation into understandable sections. In our example, we're asked to find the acceleration of a dragster. This involves applying known physics principles to reach a solution. Physics problems often require:
  • Identifying given information like initial and final conditions.
  • Selecting appropriate formulas that relate known quantities to unknowns.
  • Substituting values to solve using algebra.
Physics not only involves calculations but also requires understanding concepts and scenarios.
This helps in reasoning through the problem effectively. So next time you face a problem, remember to: read it carefully, identify key data, and understand what is being asked.
Basics of Kinematics
Kinematics is a study of objects in motion, commonly used in physics to describe the motion of vehicles, like our dragster, without considering forces that cause the motion. It's all about three main variables: velocity, acceleration, and time. Key concepts in kinematics include:
  • Velocity: The speed of the object in a particular direction.
  • Acceleration: The rate of change of velocity over time.
  • Time: The duration over which the motion occurs.
These factors are interlinked via equations known as kinematic equations.
Understanding this subject helps you grasp how fast or slow moving objects change their speed. In our exercise, knowing how acceleration connects velocity and time was crucial to solving the problem.
Application of Motion Equations
Motion equations, often called kinematic equations, are central to solving problems like finding acceleration. They help relate the parameters of motion such as displacement, initial and final velocity, time, and acceleration.Here, we used the formula: \[ a = \frac{v - u}{t} \]where:
  • \( a \)is acceleration,
  • \( v \)is final velocity,
  • \( u \)is initial velocity, and
  • \( t \)is time.
By substituting known values, we calculated the acceleration of the dragster.
This direct application highlights how understanding motion equations simplifies complex scenarios into solvable tasks. Mastering these equations equips you to handle a wide range of real-world problems with ease. Remember, choosing the right equation is as critical as the calculation itself.

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Most popular questions from this chapter

Kurt is standing on a steel beam \(275.0 \mathrm{ft}\) above the ground and throws a hammer straight up at an initial speed of \(40.0 \mathrm{ft} / \mathrm{s}\). At the instant he releases the hammer, he also drops a wrench from his pocket. Assume that neither the hammer nor the wrench hits anything while in flight. (a) Find the time difference between when the wrench and the hammer hit the ground. (b) Find the speed at which the wrench hits the ground. (c) Find the speed at which the hammer hits the ground. (d) How long does it take for the hammer to reach its maximum height? (e) How high above the ground is the wrench at the time the hammer reaches its maximum height?

A car is traveling at \(6 \overline{0} \mathrm{~km} / \mathrm{h}\). It then accelerates at \(3.6 \mathrm{~m} / \mathrm{s}^{2}\) to \(9 \overline{0} \mathrm{~km} / \mathrm{h}\). (a) How long does it take to reach the new speed? (b) How far does it travel while accelerating?

Substitute in the given equation and find the unknown quantity. \(\text { Given: }\) $$ \begin{aligned} &v_{f}=v_{i}+a t \\ &v_{f}=10.40 \mathrm{ft} / \mathrm{s} \\ &v_{i}=4.01 \mathrm{ft} / \mathrm{s} \\ &t=3.00 \mathrm{~s} \\ &a=? \end{aligned} $$

An automobile changes speed as shown. Find its acceleration. \(\begin{array}{cl}\text { Speed Change }& \text { Time Interval } & \text { Find a } \\ \end{array}\) From 0 to \(18 \mathrm{~m} / \mathrm{s}\) \(3.0 \mathrm{~s}\)in \(\mathrm{m} / \mathrm{s}^{2}\) in \(\mathrm{m} / \mathrm{s}^{2}\)

Find the velocity for each displacement and time. \(31.0\) mi west in \(0.500 \mathrm{~h}\)
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